How does exigent circmstances relate to police officers?
Basically, the idea of exigent cricumstances is that there are times when police officers do not need to abide by the requirement that they have a warrant to enter a building or take other similar actions.
In general, police officers need to have warrants in order to conduct searches, enter buildings, etc. However, there are special "exigent" circumstances in which they are allowed to do these things without warrants. The reason for this is that courts have said officers must have more leeway when they have reasonable cause to believe that someone is in danger or that evidence might be destroyed, for example.
Exigency refers to situations that law enforcement personnel may encounter. Something arising out of current events, situations that call for an immediate response, an urgent situation.
For example, a police officer has probable cause to believe that a suspect they are pursuing has fled into a building. They may enter without a warrant to effect the arrest.(warrantless entry). This is called the hot pursuit doctrine. The theory is that in a situation like this, law enforcement does not have the time to obtain a warrant. If they took the time to obtain a warrant, the suspect would flee.